Learning Causal Bayesian Networks Using Minimum Free Energy Principle

Abstract

Constraint-based search methods, which are a major approach to learning Bayesian networks, are expected to be effective in causal discovery tasks. However, such methods often suffer from impracticality of classical hypothesis testing for conditional independence when the sample size is insufficiently large. We present a new conditional independence (CI) testing method that is designed to be effective for small samples. Our method uses the minimum free energy principle, which originates from thermodynamics, with the "Data Temperature" assumption recently proposed by us. This CI method incorporates the maximum entropy principle and converges to classical hypothesis tests in asymptotic regions. In our experiments using repository datasets (Alarm/Insurance/Hailfinder/Barley/Mildew), the results show that our method improves the learning performance of the well known PC algorithm in the view of edge-reversed errors in addition to extra/missing errors.Bayesian networks (BNs) 33) are graphical models that are also called directed acyclic graphs (DAGs) and compact representations of joint probability distributions. In a DAG, its nodes and directed edges represent random variables and direct dependencies relative among variables. This combination is suitable for modeling the uncertainty surrounding random variables.

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“…Usually domain experts can determine the important variables which need to be included in the model and the links between them. The method of BNs learning consists of maximum entropy (ME) (Markham, 2011), GMMs (Bilmes, 1998;Zhang et al, 2004), and minimum free energy principle (Isozaki, 2012). Researchers apply BNs to traffic forecast with GMM (Shiliang et al, 2006), important degree analysis with K2 algorithm (Si et al, 2010), and so on.…”